Many of our sources of knowledge only afford us knowledge that is inexact. When trying to see how tall something is, or to hear how far away something is, or to remember how long something lasted, we may come to know some facts about the approximate size, distance or duration of the thing in question but we don’t come to know exactly what its size, distance or duration is. In some such situations we also have some pointed knowledge of how (...) inexact our knowledge is. That is, we can knowledgeably pinpoint some exact claims that we do not know. We show that standard models of inexact knowledge leave little or no room for such pointed knowledge. We devise alternative models that are not afflicted by this shortcoming. (shrink)

The safety conception of knowledge holds that a belief constitutes knowledge iff relevantly similar beliefs—its epistemic counterparts—are true. It promises an instructive account of why certain general principles of knowledge hold. We focus on two such principles that anyone should endorse: the closure principle that knowledge is downward closed under competent conjunction elimination, and the counter-closure principle that knowledge is upward closed under competent conjunction introduction. We argue that anyone endorsing the former must also endorse the latter on pains of (...) an unacceptable form of bootstrapping. We devise new formal models to identify necessary and sufficient conditions for these principles to hold on conceptions that construe knowledge in terms of true counterparts. These conditions state that counterparts of premise and conclusion beliefs are coordinated in certain ways whenever these beliefs stand in the relevant inferential relations. We show that the safety conception faces insuperable problems vindicating these coordination principles, because its epistemic counterpart relation is symmetric. We conclude that it thus proves unable to account for minimal closure properties of knowledge. More generally, our formal results establish parameters within which any conception must operate that construes knowledge in terms of true counterparts. (shrink)

ABSTRACT We critically review two extant paradigms for understanding the systematic interaction between modality and tense, as well as their respective modifications designed to do justice to the contingency of time’s structure and composition. We show that on either type of theory, as well as their respective modifications, some principles prove logically valid whose truth might sensibly be questioned on metaphysical grounds. These considerations lead us to devise a more general logical framework that allows accommodation of those metaphysical views that (...) its predecessors rule out by fiat. (shrink)